Galileon as a local modification of gravity
Abstract
In the DvaliGabadadzePorrati (DGP) model, the “selfaccelerating” solution is plagued by a ghost instability, which makes the solution untenable. This fact, as well as all interesting departures from general relativity (GR), are fully captured by a fourdimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar π, universally coupled to matter and with peculiar derivative selfinteractions. In this paper, we study the connection between selfacceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect—the decoupling of the scalar from matter in gravitationally bound systems—necessary to recover agreement with solarsystem tests. Our generalization involves an internal Galilean invariance, under which π’s gradient shifts by a constant. This symmetry constrains the structure of the π Lagrangian so much so that in 4D there exist only five terms that can yield sizable nonlinearities without introducing ghosts. We show that for such theories in fact there are “selfaccelerating” de Sitter solutions with no ghostlike instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshteinlike nonlinear perturbations that are also stable against small fluctuations. We investigate a possible infrared completion of these theories at scales of order of the Hubble horizon, and larger. There are however some features of our theories that may constitute a problem at the theoretical or phenomenological level: the presence of superluminal excitations; the extreme subluminality of other excitations, which makes the quasistatic approximation for certain solarsystem observables unreliable due to Cherenkov emission; the very low stronginteraction scale for ππ scatterings.
 Publication:

Physical Review D
 Pub Date:
 March 2009
 DOI:
 10.1103/PhysRevD.79.064036
 arXiv:
 arXiv:0811.2197
 Bibcode:
 2009PhRvD..79f4036N
 Keywords:

 04.50.h;
 98.80.k;
 Higherdimensional gravity and other theories of gravity;
 Cosmology;
 High Energy Physics  Theory;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 35 pages